Rewrite as a simplified fraction. ${0.2\overline{37} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 237.3737...\\ 10x &= 2.3737...\end{align*}}$ Subtracting the two equations, we have: ${990x = 235}$ ${x = \dfrac{235}{990}} $ ${x = \dfrac{47}{198}} $